arXiv subjects

Zarif Sobirov

Publications and source records attributed to Zarif Sobirov.

3 recordsLinked to original sources

arXiv2026

Cauchy Problem for the Time-Fractional Airy-Type Equation on a Star Graph with Edge-Dependent Order of Derivative

We study the Cauchy problem for a time-fractional Airy-type equation on an infinite metric star graph with edge-dependent Caputo derivatives. By constructing layer potentials generated by fractional Airy fundamental solutions, the problem is reduced to a generalized Abel integral equation. Using Pskhu's solvability results, we establish existence, uniqueness, and an explicit integral representation of the solution. The obtained framework extends previous results where identical fractional orders were assumed on all edges.

math.AP↗

arXiv2016

Sine-Gordon solitons in networks: Scattering and transmission at vertices

We consider the sine-Gordon equation on metric graphs with simple topologies and derive vertex boundary conditions from the fundamental conservation laws, such as energy and current conservation. Traveling wave solutions for star and tree graphs are obtained analytically in the form of kink, antikink and breather solitons for a special case. It is shown that these solutions provide reflectionless soliton transmission at the graph vertex. We find the sum rule for bond-dependent coefficients making the sine-Gordon equation embedded on the graph completely integrable. For the general case the problem is solved numerically and the vertex scattering is quantified. Applications of the obtained results to Josephson junction networks, DNA double helix and elastic fibre networks are discussed.

nlin.PS↗

arXiv2015

Soliton transport in tubular networks: transmission at vertices in the shrinking limit

Soliton transport in tube-like networks is studied by solving the nonlinear Schroedinger equation (NLSE) on finite thickness ("fat") graphs. The dependence of the solution and of the reflection at vertices on the graph thickness and on the angle between its bonds is studied and related to a special case considered in our previous work, in the limit when the thickness of the graph goes to zero. It is found that both the wave function and reflection coefficient reproduce the regime of reflectionless vertex transmission studied in our previous work.

nlin.PS↗